DSpace Collection: Volume 35, Number 1
http://hdl.handle.net/10525/2628
Serdica Mathematical Journal Volume 35, Number 1, 2009The Collection's search engineSearch the Channelsearch
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Denoising Manifolds for Dimension
http://hdl.handle.net/10525/2645
Title: Denoising Manifolds for Dimension<br/><br/>Authors: Jammalamadaka, Arvind K.<br/><br/>Abstract: Locally Linear Embedding (LLE) has gained prominence as a tool in unsupervised non-linear dimensional reduction. While the algorithm aims to preserve certain proximity relations between the observed points, this may not always be desirable if the shape in higher dimensions that we are trying to capture is observed with noise. This note suggests that a desirable first step is to remove or at least reduce the noise in the observations before applying the LLE algorithm. While careful denoising involves knowledge of (i) the level of noise (ii) the local sampling density and (iii) the local curvature at the point in question, in most practical situations such information is not easily available. Under the model we discuss, a simple averaging of the neighboring points does reduce the noise and is easy to implement. We consider the Swiss roll example to illustrate how well this procedure works. Finally we apply these ideas on biological data and perform clustering after such a 2-step procedure of denoising and dimension reduction.<br/><br/>Description: 2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.A New Hereditarily l^2 Banach Space
http://hdl.handle.net/10525/2643
Title: A New Hereditarily l^2 Banach Space<br/><br/>Authors: Petsoulas, Giorgos<br/><br/>Abstract: We construct a non-reflexive, l^2 saturated Banach space such that every non-reflexive subspace has non-separable dual.<br/><br/>Description: 2000 Mathematics Subject Classification: 46B20, 46B26.The Legendre Formula in Clifford Analysis
http://hdl.handle.net/10525/2641
Title: The Legendre Formula in Clifford Analysis<br/><br/>Authors: Laville, Guy; Ramadanoff, Ivan<br/><br/>Abstract: Let R0,2m+1 be the Clifford algebra of the antieuclidean 2m+1 dimensional space. The elliptic Cliffordian functions may be generated by the z2m+2 function, analogous to the well-known Weierstrass z-function. The latter satisfies a Legendre equality. We prove a corresponding formula at the level of the monogenic function Dm z2m+2.<br/><br/>Description: 2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications
http://hdl.handle.net/10525/2638
Title: Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications<br/><br/>Authors: Mejjaoli, H.<br/><br/>Abstract: In this paper, we study the Schrödinger equation associated with the Dunkl operators, we study the dispersive phenomena and we prove the Strichartz estimates for this equation. Some applications are discussed.<br/><br/>Description: 2000 Mathematics Subject Classification: 35Q55,42B10.Structure of the Unit Group of FD10
http://hdl.handle.net/10525/2635
Title: Structure of the Unit Group of FD10<br/><br/>Authors: Khan, Manju<br/><br/>Abstract: The structure of the unit group of the group algebra FD10 of the dihedral group D10 of order 10 over a finite field F has been obtained.<br/><br/>Description: 2000 Mathematics Subject Classification: 16U60, 20C05.Uniform G-Convexity for Vector-Valued Lp Spaces
http://hdl.handle.net/10525/2632
Title: Uniform G-Convexity for Vector-Valued Lp Spaces<br/><br/>Authors: Boyko, Nataliia; Kadets, Vladimir<br/><br/>Abstract: Uniform G-convexity of Banach spaces is a recently introduced natural generalization of uniform convexity and of complex uniform convexity. We study conditions under which uniform G-convexity of X passes to the space of X-valued functions Lp (m,X).<br/><br/>Description: 2000 Mathematics Subject Classification: 46B20.